M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 16
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S. Haldane, “Pasteur and Cosmic Asymmetry.” Nature 1960, 185, 87.63. L. Pasteur, C. R. Acad. Sci. Paris, June 1, 1874.64. Orgel, The Origins of Life.65. Ibid.66. L. Carroll, Through the Looking Glass and what Alice found there; See, e.g., inThe Complete Illustrated Works of Lewis Carroll. Chancellor Press, London,1982, p. 127.67. See, e.g., G. W. Muller, “Thalidomide: From Tragedy to New DrugDiscovery.” Chemtech 1997, 27(1), 21–25.942 Simple and Combined Symmetries68. See, e. g., E. L.
Eliel, “Louis Pasteur and Modern Industrial Stereochemistry.”Croatica Chemica Acta 1996, 69, 519–533.69. P. Ahlberg, “The Nobel Prize in Chemistry.” In Les Prix Nobel—The NobelPrizes 2001, Almquist & Wiksell International, Stockholm, 2002, p. 20.70. See, e.g., S. C. Stinson, “Chiral Drugs.” Chem. Eng.
News 2000, October 23,55–78; S. C. Stinson, “Chiral Pharmaceuticals.” Ibid. 2001, October 1, 79–97;A. M. Rouhi, “Chiral Business.” Ibid. 2003, May 5, 45–55; A. M. Rouhi,“Chirality at Work.” Ibid. 2003, May 5, 56–61; R. Winder, “Pure enzymes.”Chemistry & Industry. 2006, June 5, 18–19; C. O’Driscoll, “Reflective Work.”Ibid. 2007, May 7, 22–25.71. A. V. Shubnikov, V. A. Koptsik, Symmetry in Science and Art, Plenum Press,New York and London, 1974. Russian original: Simmetriya v nauke i isskustve,Nauka, Moscow, 1972.72.
Ibid.73. F. A. L. Anet, S. S. Miura, J. Siegel, K. Mislow, “La-Coupe-Du-Roi and ItsRelevance to Stereochemistry – Combination of 2 Homochiral Molecules toGive an Achiral Product.” J. Am. Chem. Soc. 1983, 105, 1419–1426.74. M. Cinquini, F. Cozzi, F. Sannicoló, A. Sironi, “Bisection of an AchiralMolecule into Homochiral Halves – The 1st Chemical Analog of La Coupedu Roi.” J. Am. Chem. Soc. 1988, 110, 4363–4364.75. Ibid.76. Anet et al., J. Am. Chem. Soc.
1419–1426.77. Cinquini et al., J. Am. Chem. Soc. 4363–4364.78. Anet et al., J. Am. Chem. Soc. 1419–1426.79. H. S. M. Coxeter, Regular Polytopes, Third Edition, Dover Publications, NewYork, 1973.80. Weyl, Symmetry, p. 74.81. Coxeter, Regular Polytopes.82. N. V. Belov, Ocherki po strukturnoi mineralogii (in Russian, Notes on structural mineralogy), Nedra, Moscow, 1976.83. Häckel, Kunstformen der Natur.84.
J. Kepler, Mysterium cosmographicum, 1595.85. Häckel, Kunstformen der Natur.86. A. Koestler, The Sleepwalkers, The Universal Library, Grosset and Dunlap,New York, 1963, p. 252.87. Kepler, Mysterium Cosmographicum.88. T. Saito, A. Yoshikawa, T. Yamagata, H. Imoto, K. Unoura, “Synthesis,Structure, and Electronic Properties of Octakis(3 -sulfido)hexakis(triethylphophine) hexatungsten as a Tungsten Analogue of the Molecular Model for Superconducting Chevrel Phases” Inorg.
Chem. 1989, 28,3588–3592.89. Ibid.90. A. Müller, P. Kögerler, A. W. M. Dress, “Giant Metal-Oxide-Based Spheresand Their Topology: from Pentagonal Building Blocks to Keplerates andUnusual Spin Systems.” Coord. Chem. Rev. 2001, 222, 193–218.References9591. Coxeter, Regular Polytopes; L. Fejes Tóth, Regular Figures, Pergamon Press,New York, 1964.92.
Ibid. and H. M. Cundy, A. P. Rollett, Mathematical Models, Clarendon Press,Oxford, 1961; M. J. Wenninger, Polyhedron Models, Cambridge UniversityPress, New York, 1971; P. Pearce, S. Pearce, Polyhedra Primer, Van NostrandReinhold Co., New York, 1978.93. Cundy, Rollett, Mathematical Models.94. N. Copernicus, De Revolutionibus Orbium Caelestium, 1543, as cited in G.Kepes, The New Landscape in Art and Science, Theobald & Co., Chicago,1956.95.
W. M. Meier, D. H. Olson, Atlas of Zeolite Structure Types, Third RevisedEdition, Butterworth-Heinemann, London, 1992.96. B. Beagley, J. O. Titiloye, “Modeling the Similarities and Differences betweenthe Sodalite Cages (Beta-Cages) in the Generic Materials - Sodalite, Zeolitesof Type-A, and Zeolites with Faujasite Frameworks” Struct.Chem. 1992, 3,429–448.97. Ibid.98. W. P.
Schaefer, “The Snub Cube in the Glanville Courtyard of the BeckmanInstitute at the California Institute of Technology.” Chemical Intelligencer1996, 2(4), 48–50.99. I. Hargittai, “Imperial Cuboctahedron.” Math. Intell. 1993, 15(1), 58–59.100. S. Alvarez, “Polyhedra in (Inorganic) Chemistry.” Dalton Trans. 2005,2209–2233.Chapter 3Molecular Shape and GeometryForm is a diagram of forces.D’Arcy W. Thompson [1]A molecule is a collection of atoms kept together by interactionsamong those atoms.
For some purposes it is better to consider themolecule as consisting of the nuclei of its constituent atoms andits electron density distribution. Generally, it is the geometry andsymmetry of the arrangement of the atomic nuclei that is consideredto be the geometry and symmetry of the molecule itself. At a certainpoint in science history, spatial considerations entered the descriptionof molecules. While we take this for granted today, the first steps inthis direction were not without hurdles. The year 1874 was the birthof stereochemistry although the term itself was only introduced aslate as 1890, by Victor Meyer to describe the three-dimensional positions of the atoms in a molecule.
The basic concepts were proposedby J. H. van ‘t Hoff and J. A. Le Bel, and van ‘t Hoff published abooklet called La Chimie dans l’Espace (Chemistry in Space) [2].When the two scientists suggested the idea of the tetrahedral geometrical arrangement of the bonds radiating from the carbon atom, itwas revolutionary, and some found it too radical. The most vocalcritic of the new views was an outstanding organic chemist, HermannKolbe, who ridiculed van ‘t Hoff in the most blatant way [3]. Thetrue breakthrough came with X-ray crystallography, which yielded alarge amount of direct structural information.
In time, other powerfultechniques joined in and modern structural chemistry commenced.Theories and models appeared in parallel with the growing amountof experimental data, and the observation of trends and regularitiesgreatly facilitated the development of this new field of chemistry [4].M. Hargittai, I. Hargittai, Symmetry through the Eyes of a Chemist, 3rd ed.,C Springer Science+Business Media B.V. 2009DOI: 10.1007/978-1-4020-5628-4 3, 97983 Molecular Shape and GeometryMolecules are finite figures with at least one singular point intheir symmetry description.
Thus, point groups are applicable tothem. There is no inherent limitation on the available symmetries formolecules. Molecules in the gas phase are considered to be free. Theyare so far apart that they are unperturbed by interactions from othermolecules and thus can be considered isolated from each other. Onthe other hand, intermolecular interactions may occur between themolecules in condensed phases, i.e., in liquids, melts, amorphoussolids, or crystals. In the present discussion all molecules will beassumed unperturbed by their environment, regardless of the phaseor state of matter in which they exist.Molecules are never motionless. They are performing vibrations allthe time. In addition, the gaseous molecules, and also the moleculesin liquids, are performing rotational and translational motion as well.Molecular vibrations constitute relative displacements of the atomicnuclei with respect to their equilibrium positions and occur in allphases, including the crystalline state, and even at the lowest possibletemperatures.
The magnitude of molecular vibrations is relativelylarge, amounting to several percent of the internuclear distances. Typically, there are about 1012 –1014 vibrations per second.Symmetry considerations are fundamental in any description ofmolecular vibrations, as will be seen later in detail (Chapter 5).First, however, the molecular symmetries will be discussed, ignoringentirely the motion of the molecules.
Various molecular symmetries will be illustrated by examples. A simple model will also bediscussed to gain some insight into the origins of the various shapesand symmetries in the world of molecules. Our considerations willbe restricted, however, to relatively simple, thus rather symmetricalsystems. The importance and consequences of intramolecular motioninvolving relatively large amplitudes, will be commented upon in thefinal section of this chapter.3.1. IsomersThe empirical formula, or sum formula, of a chemical compoundexpresses its composition. For example C2 H4 O2 indicates that themolecule consists of two carbon, four hydrogen and two oxygenatoms. This formulation, however, provides no information on the3.1.
Isomers99order in which these atoms are linked. This particular empiricalformula may correspond to methyl formate (3-1), acetic acid (3-2),and glycol aldehyde (3-3). Only the structural formulae for thesecompounds, shown below, distinguish among them. This is calledstructural isomerism.Although these molecules, as a whole, are not symmetric, someof their component parts may be symmetrical. They possess what iscalled local symmetry.
Similar atomic groups in different moleculesoften have similar geometries, and thus similar local symmetries. Thestructural formulae reveal considerable information about these localsymmetries, or at least their similarities and differences in variousmolecules. The above simplified structural formulae are especiallyuseful in this respect. This approach is widely applicable in organicchemistry, where relatively few kinds of atoms build an enormousnumber of different molecules. A far greater diversity of structuralpeculiarities is characteristic for inorganic compounds.The symbol for the carbon atom occurs twice in all three simplifedstructural formulae above, a fact that indicates differences in the structural positions of these carbon atoms. The same applies to the oxygenatoms.
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